Organizing Uncertainty does not eliminate it
Product Description
The DATARRAY Process. DATARRAY is a
process that is applied to arrays of loss development history. It produces an empirical frequency
distribution of all possible outcomes of aggregate ultimate losses resulting from the application of the loss development method.
More specifically, DATARRAY is an approximation algorithm for creating the frequency distribution of all possible outcomes,
as produced by the application of the loss development method
when using the observed loss development factors (LDFs). It can be produced to any degree of precision desired by the user.
DATARRAY produces individual distributions for individual data sets as well as the convolution distribution that combines the
outcomes of two or more component distributions.
Input. DATARRAY operates on any configuration of loss development data. The DATARRAY input can be a triangle, a trapezoid, a parallelogram, or an irregular array of loss development data. Moreover the types of data contained in the array of raw data can be of any of the customary types of data: reported losses, paid losses, loss ratios, frequencies, severities, direct or net, basic limits or excess loss experience, etc.
Calculations. DATARRAY derives the equivalent of the calculations that would be made if one calculated every single possible outcome using all permutations of age-to-age loss development factors. The degree of accuracy is specified by the user. The number of calculations involved in creating a true distribution (e.g., calculating all possible loss development outcomes) is simply too large to even contemplate. For example, if one had a 10X10 loss development triangle (e.g., the same size as a typical schedule P loss development triangle), and five different tail factors, the number of iterations needed to produce the actual distribution associated with with this data set is 9.2X1021. Even a computer that can calculate 1 billion iterations per second would need 290,927 years to complete the process of creating all possible outcomes, a physical impossibility. DATARRAY, on the other hand through the use of the approximation algorithm, produces the functional equivalent of the actual distribution to within any desired degree of accuracy.
Output. DATARRAY produces a frequency distribution of the approximated set of outcomes. The output is in both tabular and graphic formats. The specific output consists of the following elements: (1) a table of all approximated outcomes along with their associated frequencies, (2) a table of all approximated outcomes along with their associated cumulative frequencies, (3) the mean and standard deviation of the frequency distribution, (4) a graph of the frequency distribution, and (5) a graph of the cumulative frequency distribution.
Flexibility. Two points illustrate the vast range of possibilities that are embedded in the above summary description:
Input. DATARRAY operates on any configuration of loss development data. The DATARRAY input can be a triangle, a trapezoid, a parallelogram, or an irregular array of loss development data. Moreover the types of data contained in the array of raw data can be of any of the customary types of data: reported losses, paid losses, loss ratios, frequencies, severities, direct or net, basic limits or excess loss experience, etc.
Calculations. DATARRAY derives the equivalent of the calculations that would be made if one calculated every single possible outcome using all permutations of age-to-age loss development factors. The degree of accuracy is specified by the user. The number of calculations involved in creating a true distribution (e.g., calculating all possible loss development outcomes) is simply too large to even contemplate. For example, if one had a 10X10 loss development triangle (e.g., the same size as a typical schedule P loss development triangle), and five different tail factors, the number of iterations needed to produce the actual distribution associated with with this data set is 9.2X1021. Even a computer that can calculate 1 billion iterations per second would need 290,927 years to complete the process of creating all possible outcomes, a physical impossibility. DATARRAY, on the other hand through the use of the approximation algorithm, produces the functional equivalent of the actual distribution to within any desired degree of accuracy.
Output. DATARRAY produces a frequency distribution of the approximated set of outcomes. The output is in both tabular and graphic formats. The specific output consists of the following elements: (1) a table of all approximated outcomes along with their associated frequencies, (2) a table of all approximated outcomes along with their associated cumulative frequencies, (3) the mean and standard deviation of the frequency distribution, (4) a graph of the frequency distribution, and (5) a graph of the cumulative frequency distribution.
Flexibility. Two points illustrate the vast range of possibilities that are embedded in the above summary description:
- Weighted or unweighted calculation. The distribution can be produced on a weighted or unweighted basis. The weights may
be set in any number of ways to emphasize various elements of the historical experience.
- Adjusted Data. DATARRAY may be run on unadjusted or adjusted data (e.g., data adjusted per the Berquist-Sherman family of methodologies). In this manner the distribution produced by the unadjusted data can serve as a default distribution against which the distribution produced by the adjusted data may be compared to determine the effect of using adjusted data.
Applications.
At the highest level, the main application of DATARRAY is that it provides a consistent and assumption-free framework for quantifying and communicating to and
with others about the issue of the variability of loss reserve estimates. More specifically, some key applications of DATARRAY are: (1) identifying the basis
for selecting ranges of reasonableness, (2) assigning a probability of sufficiency to a particular reserve estimate, (3) identifying the impact on the
distribution of using adjusted data to derive reserve estimates, (4) identifying the risk margin that is built into rates, (5) assisting in the pricing
of reinsurance covers. For more information on how these distributions may be used read "Probabilistic Framework for Evaluating Materiality and Variability in Loss Reserve Estimates".
This is a paper written by Irene Bass and C. K. Stan Khury and published in the Casualty Actuarial Society 2003 Forum.
Other applications include: quantifying and assigning meaning to the amount that is commonly called “a margin for adverse deviation” and assessing the sufficiency of an insurer's surplus with respect to the impact of reserve variability.
Availability. Bass & Khury offers a service that can provide interested users with the output of DATARRAY for their data. See “Ordering Information” page.
Limitations. The user of the DATARRAY output needs to keep some limitations in mind:
Actual Applications. The following list is a sampling of actual applications that Bass & Khury has performed using outputs of the DATARRAY process:
Other applications include: quantifying and assigning meaning to the amount that is commonly called “a margin for adverse deviation” and assessing the sufficiency of an insurer's surplus with respect to the impact of reserve variability.
Availability. Bass & Khury offers a service that can provide interested users with the output of DATARRAY for their data. See “Ordering Information” page.
Limitations. The user of the DATARRAY output needs to keep some limitations in mind:
- DATARRAY is not a reserving methodology.
- DATARRAY has no natural application to mass tort reserving.
- DATARRAY does not necessarily recognize forward changes in the environment.
Actual Applications. The following list is a sampling of actual applications that Bass & Khury has performed using outputs of the DATARRAY process:
- Reinsurance. Test the reasonableness of the price of an excess of loss cover.
- Private Passenger Automobile Liability. Estimate the probability of adequacy of a reserve estimate.
- All Lines. Test the reasonableness of a loss reserve estimate set by an MGA on behalf of members of a reinsurance pool.
- All Lines. Test the effect of Berquist-Sherman type adjustments on the variability of loss reserves.